- #1
Argelium
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Homework Statement
Having a conducting sphere with radius ##R## and charge ##Q##, dielectric is put on it so that a spherical shell with inner radius ##R## and outer radius ##3R## is formed. Calculate:
1. Electric permitivitty ##\epsilon## such that ##E(r), R<r<3R## is constant and there's no polarisation charge on the surface of radius ##3R##.
Homework Equations
$$\iint \vec{D} \cdot d\vec{S} = Q_{free}$$
$$\iint \vec{P} \cdot d\vec{S} = -Q_{bound}$$
$$\vec{D} = \epsilon_0 \vec{E} + \vec{P}$$
The Attempt at a Solution
So, if there's no polarisation charge we have that on ##r=3R##:
$$\iint \vec{P} \cdot d\vec{S} = -Q_{bound} = 0$$
And then ##\vec{P} = 0## and:[/B]
$$D = \epsilon_0\frac{Q}{4\pi\epsilon (3R)^2} $$
Since we want it constant, then for ##R<r<3R##:
$$D(r) = \frac{Q}{4\pi(3R)^2} = \epsilon_0\frac{Q}{4\pi\epsilon r^2}$$
And then
$$\epsilon (r) = \frac{\epsilon_0}{(3Rr)^2} $$
However I'm not sure, cause ##P## is not supposed to be 0 in that zone. But if it isn't, how do i calculate ##P##?
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